Sometimes people say that ,dkjr fvhjh d8:s2+10mju5i jwater is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is w :r501jjkd8 j2uj ,d+vsimhhfrong with this statement?

Will the acceleration of a car be the same when the car travels around a sgrk -so41/ gfzr toog 9n)xry1e9;dh.harp curve at a constant 60 km/h as when it travels ar khxg -trzgr;.og/n9sy)e4od1o1 f9round a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hiyqps3rau9gl u: /v/) plly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level gasp /3r:vy p9qu/ul )stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. W0j 3a6; zndzx2vjxh p-hich of these forces prov -xj6z axnj0;vzhd 2p3ides the centripetal acceleration of the child?

A bucket of water can be whirled in a vert+em/k.p jze7i ical circle without the water spilling out, even at the top of the circle when the buck7+mejkpei/ z.et is upside down. Explain.

How many “accelerators” do you have in yotvf6h3da f, 1f :cp8oyur car? There are at least three controls i:,d1 fv6yf ct fph3o8an the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cwnf5by6t td s5+ *jd7sp:p9dbrest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explainp:bts dt6 sd+ y55 p*jdf79wnb this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speedx4 wqc3-v8je rcp9vlsi9)p3 7ls kgv *?

Why do airplanes bank when they turn? How wouldgv:h9e7qn cv 9 you compute the banking angle given its e:7qh9vc9vg nspeed and radius of the turn?

A girl is whirling a ball on a string ao * yuge x.fe:+v,5ayuround her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hiaf. x y*o:uy+e,eug5 vt a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth?hkqgbfsy;rl w0 45s/, If so, how large a force? Consider h,5 qy/0b4;fgrksswl an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass uwxjl,mhu /r565*rn k were double what it is, in what ways would the Moon’s orbit l 6n k5*hxmru5j uw,/rbe different?

Which pulls harder gravitationally, the Earth on the skl y7jj n+ -0.yy8vuw p( f3gt*xy5eeMoon, or the Moon on the Earth? Which accele w fs3p(tygk u5+vlyej*-jen .7x yy80rates more?

The Sun's gravitational pull on the Earth is much larger than the ljp52:xtqxujh/w9zw 2i* n+eMoon's. Yet the Moon's is mainly res 2pwx9tj2+n*z5u xlj heiqw:/ponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator 81*b qdoqy3rk or at the poles? What two effects are aqrq1 *oyk 3bd8t work? Do they oppose each other?

The gravitational force on the Moon due to the Earth hass 7jp1(+( .) r kbmbruj6szis only about half the force on the Moon due to the Sun. Why isn’tr7abkjhss )r1ps(ub(zj+6 m. the Moon pulled away from the Earth?

Is the centripetal acceleratio7w2(2i:mf74qprz;gotlso ff f 3 dnv9n of Mars in its orbit around the Sun larger or smaller than the cen3m:qgfpv7 7(oro;ft 2f2d l4f9w znis tripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east oe f-xbl4x1e y -pl*,pur (b) toward the west? Consider the Earth’s ro-b1pylp * u xele,fx4-tation direction.

When will your apparent weight be the greatest, as measured by a scale in a vww4tkr pa, ax ev6 d(29l2g1kmoving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward atw,xkva2 1r t4l9g26k evdwpa( constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected by27j g/d)m1gz ldnt- dcsh*:hc weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspect:thhc/gs nd-j2z1 )7 lg *cdmds of gravity you can think of.

Explain how a runner experiences “free fall” ornv 8z*l qlop;yel8h29 “apparent weightlessness” between sty*l ;8lve ol9hp8 n2qzeps.

The Earth moves faster in its orbit around the Sun in Januaseosf daq)t2 z x/1(u+h1eu;lry than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in prod1ze 1saq;fo/ lsx+uue2(htd )ucing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it wab w3 zsv 17nl;o-ynlc3s discovered to have a moon. Explain how this discovery enabled an el ny7 onv1-szl;w 3c3bstimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. ag4nl.g0n*x7x2erk m Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A chiakr mnxg*.eln47 0xg2ld sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 b pq63w1mzg) *p -lhpb$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal accz0id 9+d ga2jteleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbja9g+ t2 zd0diit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a sukle6ub(;k(aur 5w yl35p x62.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Ck;6 (ybkxa l35(e5sl p 6uwurualculate the speed of the discus.   

  Suppose the space shuttle is in orbi8xxn31 w4ps3fntsbr , t 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational ans rns8xb,3p 14wtf3xcceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of 6 r7ac7ivksj/clay on the edge of a potter’s wheelrsaic/7j6 v 7k turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a xs 3e7f 4*hzyqtnva2*-6wbomstring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed ite6wmnx 24qyso-a**h v f3zb7s 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn oy9dmo( (of3cp km4b-tf radius 77 m on a flat bpt34ykc(-9f o d(ommroad if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be,:;yt;qrg h o1s01 bcexy t-ki between the tires and the road if a car is to round a g0:qc1tb1;t ky s;-xh reo,iy level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet figh )o1buqjq-1qpl)vuvlz;e k7)ter pilots is designed to rotate a trainee in a hql) oj 7v) 1ep1 -);kvzququlborizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from b95 u-sr1exe/lt q fa7the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the co r1-be qa/xuel5 ft7s9in remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mziecz:kurm v;)1*eye24 i+c kust a roller coaster be traveling when upside down at the tvc e4z;i+y :re*u12k )mckei zop of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses th4 ;om /8lpb 4 -a*jjrjlnama-pe rounded top oj j4aja m8l- o4;plrabnp-m/*f a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Fe(bih+wob-c+z q* 7 lzarris wheel need to make for the passengers to feel “weightless” at the i* 7b+bzz- lhaqo +c(wtopmost point?    rpm

  A bucket of mass 2.00 kg is whirled inv6-0 xz3aosdbc d 3j5r a vertical circle of radius 1.10 m. At the lowest point of its motion the tensioj-vasc 3zo06 rbxd5d 3n in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotcz r3/v -t..crcy1xgiwn; sfaxm0 v16ate if a particle 9.00 cm from the axis of rotation is to experience an accel-i16 .z1cr 3tvrw/x cfxy;as0vgm.nc eration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa11k8x spq v4kvlled "room1s kvk4x8p qv1." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) i 8/z gj-oj9 ifdgu 41:tje*lals rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5/ zi1jfj 4jol89 udag*:el -tg-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not igno/9 :*e g cinbmg9wubpu7m60p uring the weight of the ball which revolves on a string 0.600 mep :0* gi6/pb99 mbug7mcnu wu long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is pe-xkegp) m -as a(;r3jprfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesgbuk npq .b3tqc 9 g)p3wp/ef9)ux7 /n $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasit o52nxlrv:g3 g,:++hp vbniwve maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components hj7f8.ug k8qqof the net force exerted on the qh 8 .fq8kj7ugcar (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 50(ed u;;q 9eslz+;wmbd0 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this ac;q9+(esel ;bm d;wd zuceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle orz(lcd)pq +7zf radius 2.90 m . At a particular in)l(r+cz p qz7dstant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth rap s fb:f 7pjuh. ak6),a/4cuobdii) above the Earth’s surface if its mass is 135uj.ku/s:)46paffpb7 bc, h oa 0 kg.   

  At the surface of a certain planet, the gravitat7- 7 r3.uy p sgyft/d(ya1eyohional acceleration g has a magnitude r-7 ypyyads7/fe h(gu yt3o1. of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The3me 8/o pjr5xq Moon's radius is 1.748x3jrpo 5m/ eq $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tahtudk* j72,6 oboq a 0s-k)roimes that of Earth, but has the same mass. What is the acceleration due to gravity near its sur -t usjbqh70oa62 ,do ok)rk*aface?   

  A hypothetical planetu h0o:g ehgp+,ke. zb. has a mass 1.66 times that of Earth, but the same radius. What is gpueg+:. hk.ez bho0g, near its surface?   

  Two objects attract eac stbc5 ml klfo3c.vg*hbg;v+;(,g, edh other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of graq cfx4ut-mk /ry+5 ps*h tj0z*vity, at (a) 3200 m *jk u*t4s-yr mt 50z+/pchxfq   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fromz 5n3 ncn*u;g 73mqclre5s) tu the Earth’s center to a point outside the Earth where thegravitational accelera *73scm uzq)n5 gtlne; cnu53rtion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pac ) oege5eprgj: yo4j:*ked into a sphere aoj:j yo ere: gp4e)*g5bout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average wty /i 1ei(mpzn+ya z8gfh01* star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What ifzz1n8a+wi0 mpi1 (/yh ty* ges the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in thj*x i7cd g3i w/6jgc9: rj nbca9xl7p3e space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and cb 6lr/wajg9 7 nijc: c 37xp3j*xdi9gyourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locb /63bwg-m0a/p /ur f 7aussngated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exertedbmgg/r/s3a7au bsufw /n6- p 0 on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planbv uxn-k p c api5mg,6+wh1z./ets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, , w i5vacpkph x+mzb1.-6/n guassuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of -qqf a;5 7fcpjbb+rm)what it is on Earth, and that Mars’ radius is 3400 km, determine the masap bfq-bq;jfr5 7)+cm s of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val7e9qp;z b 4no6xhq.m tue for the period of the Earth and its di4xe ob q7z9t6 p.;mqnhstance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular9dnut o6nl 57l(clq5l orbit about the Earth at a height olqul ncl9(n56t5 7odlf 3600 km.    $\times 10^3$

  The space shuttle relf(o 7h) +f/ioxxh)qxdeases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? xf) xd+qf7) ih hoo(x/    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experie a ;vsvem5ic-ou81*q dn/ /anlnce simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and givec ov ;-dm/eu/lv n8aqa5sin *1 your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satel8* k hxxaqe(.e3)e3 eaf4xejlda w4+llite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of thfa)lwaak e3 ele exhx d3(j48.e* xq4+e Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocityq8;9 u d/erjb ykeiq*/ would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit aroiyrqe/j/;* u98 kdqebund the Earth?   

  During an Apollo lunar landing mission, the com6c*ql3p 1s qsk,wne;ymand module continued to orbit the Moon at an altitude of about 100 kw1eq,y*q c n3pls k;6sm. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of iht1u,aq z 1 vma*aed4(ce that orbit the planet. The innera4ze(vaa hu1*1d tqm, radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m i g/ 8*3:wcn3nf29vtbqzh up bnn diameter rotates once every 15.5 s (see Fig. 5–9). What is t3w gn2uh3t/fpqbb8v nn9:zc*he ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a ws9e/;no0 k 0dlsoite4pp. 3s 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant veloci0 p 0kw oie3e94ops;l.sstnd /ty,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two sh a1t*/iu7upeurbghr13- 9w x tars of equal mass. They are observed to be separatedu1/ax e3g bw91 u-7hrpt u*hir by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in h0 q s/dmq j0m,vjzp)9k00jzr.gc ws5; si)it an elevator that dwrcs j)kp sit)jjg0 q0.q /hmv;,z9sz m005i moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from aicm 2(qf-h 3h frwgzx*zfp(- ) cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator z zfh3fx -wm(p*h-fq)g2(rciaccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very neae :o)sokg5wr 2r the surface of a planet with period T , the densio) 2owrskge:5 ty (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the perq-q5 +h/nkjl yiod of an artificial satellite orbiting very near the Earth q/-5k j+hqnly’s surface.    s

  The asteroid Icarus, though onlp t.(kftex -urb w(/r9y a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. Whke-x.urfr (9btpt /( wat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc5 y-hac ng +s4))c);pvirld b0wgng0ae of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every zy)y)j; + kj7tb0(emo gik;rg76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance frmy ky;tzge+)gr );k 7ojb0 j(iom the Sun.]    $\times 10^6$

  Our Sun rotates about thhzi r,)j6vm-d (2tnlh e center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the d;q t t r13wmnhvzd863four largest moons of Jupiter (those di1z6mdvwnt8 3qr;tdh3scovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and d1.ewn jmu uey30n g -odyn14r.istance of the Moon. e mu0dn1eywn-o4.njur13y. g    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,rurpf +vqc*+k;v4s t9 using Kepler’s third law. Use 9ru+c ; vqk* v+fprs4tthe distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists+a;r5 t9 ikt7hvuz)ve e- g;el of many fragments (which some space scientists think came from a planet that once orbited the Sun bu ee7+i5zkgt ;ae hv-vt;lr9)ut was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describ zz3i8fbe gbwg9 66ea*iu**etes an artificial "planet" in the form of a band completely encircling a sun (Fig. *6aze g*u eg tib*ei9z6bf83w5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a8kt88q erohrf2 oc4n 7 hanging vine (Fig. 5–41). If his arms are capable of exertin 8r72ofqre8kco8 4 htng a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hy + q1o7g mng:ssz,s;palf what it is on the ,7ygpz:n 1;gs omssq +surface?    $\times 10^6$

  On an ice rink, two skatera* wcn/ h82ehns of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms arech8hne w /a2*n each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity ahj *q)e ):ruh8u(dnk ct the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnit))rjn c:*ehu q8d(uh kude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wil+ecisp) 9s6ikw+h*lt/m.t r4wwyjn2l a spacecraft traveling directly from the Earth to the Moon experi2t)j w+s pisw/lhc i6r9tw +*.ky nm4eence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bu;gk/ *lt zr1 jj4de,xknxkxe 3*hkl65 t when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceler6gr4* ,/;*xjxnl1 kd ljk 5k zhektx3eation of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consids p (e6f0paum4/z bc2sts of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation sp4p2dpe /ma csu0bfz(6 eed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fi1r*lk0yg j 7r n)w f3b lw;vzlv3opu2*g. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, thu9rr6 x3q+bqze acceleration due to gravity at its surfaceq3r 9q+xbur6 z and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected frxxl8nh *7/k,n+:ok ahqr jg1 rom the vertical by an ang/ 7gk nk1*r,8:rax+hn qolxjhle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coe+d ncdkf9kw ,r*ws /+efficient of static frf9cw +,sw *+d/erkkndiction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects awr:e2:2 bdmmw t the equatob we2rwmdm2 ::r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 e2wa.s i.s+aj4.bzun$\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curvm82,m q el:xv0f5tviq e of radius 235 m. A lamp suspended from the25 tv:,eqil m0 qvfxm8 ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thu5qc *dvpu iea6 wp3.,ps, it has been claimed that a person would be cr5aqcpu3p ,.edp6*wv iushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the prese l 6tkmz,h8hc(nce of an extremely massive core in the distant galaxy M87, so dense that it could be a bkc,ltz (6hm h8lack hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valleyo 9d4pde2d4yzb/fy q z z1)oi; shown in Fig. 5–45. Both the hill and valley have a radius of curvatqod/e 412i zzd;9 ybdz)fy4opure R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 sq7 mo6z,qcv8datellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine 68q z,o qdvcm7the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendig,ip -4 nffrmse:z3s/ /nntc;ey6.xn t0)kiezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height ofk- 6/n 3:pe.yc mf;z0srxnsn )if4i net/,tgi about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pig8qmwk (8+q . rtv/cm0ti-xn ursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400i.q-tk gt (8qxr8 0nwm+/cvmi km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dis8c x5tq+m qddjfz1 d2huf.)2btance from the Su2fhx q u+dd5zcd8) qb.m ftj12n?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you *; moquh;z2k w8kup5q could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assupzo*8k qwu k;u2;5qm hmptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Ga5c/rm5lp )7nbl kqfc .laxy (Fig. 5-46) at a distance of about 30,000 light-years from the centr)75k.pcqf/ b5c mllner $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a squqeq lmr9i fa-.c 0wz,8bvt-e,are 0.50 m on each side. Find the magnitude and direction of the gravit8,f- qz, ait w-rbqm0veel9.cational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartb.jf5ch(wf4or 7 0 kboh $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the accelerae/tojzjy49 4i+d 1a3zgr)vyz tion experienced by the tip of the 1.5-cm-long sweep second hand on yz943)+4jd/ iazr y ygjoe1vtzour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and st4msr*mum- ,ksr( j t2rart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the firsu2kjr4 tm-m,m (* srshing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hig6vpf toztr2qacx 6. 5mkml9k( ,eym +9hway is designed so that a car traveling a99 6xp .cqt(m mkto5,erl+vk m a2yf6zt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, 0i58btm 0+eegee3mxxutilizes tilt of the cars when negotiating curves. The angle of tilt is mx ib 03em+e50tge8xeadjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$